We have determined new rotation periods for 404 stars in the Orion Nebula Cluster using the Wide Field Imager attached to the MPG/ESO 2.2 m telescope on La Silla , Chile . Mass estimates are available for 335 of these and most have M < 0.3 M _ { \odot } . We confirm the existence of a bimodal period distribution for the higher mass stars in our sample and show that the median rotation rate decreases with increasing mass for stars in the range 0.1 < M < 0.4 M _ { \odot } . While the spread in angular momentum ( J ) at any given mass is more than a factor of 10 , the majority of lower mass stars in the ONC rotate at rates approaching 30 % of their critical break-up velocity , as opposed to 5-10 % for solar-like stars . This is a consequence of both a small increase in observed specific angular momentum ( j=J/M ) and a larger decrease in the critical value of j with decreasing mass . Perhaps the most striking fact , however , is that j varies by so little - less than a factor of two - over the interval 0.1-1.0 M _ { \odot } . The distribution of rotation rates with mass in the ONC ( age \sim 1 My ) is similar in nature to what is found in the Pleiades ( age \sim 100 My ) . These observations provide a significant new guide and test for models of stellar angular momentum evolution during the proto-stellar and pre-main sequence phases .